“To come back after so long away and be so warmly received means so much,” she said.
The star, who closed the show by performing When We Were Young, also received best British single and the Global Success award.
The show also featured an emotional tribute to David Bowie, led by Annie Lennox and his friend Gary Oldman.
Lennox called Bowie, who died of cancer last month, “a quintessential visionary” and “the ultimate iconoclast.”
Oldman then accepted a Brits icon award on behalf of the singer and his family.
“David you were mortal, but your potential was superhuman,” he said, “and your music lives on”.
Bowie’s band then performed a medley of his hits, before New Zealand singer Lorde joined them to sing Life On Mars.
The ceremony was opened by Coldplay, who gave a colourful, floral performance of their single Hymn For The Weekend, showering the audience with confetti petals as they played on one of two separate stages at London’s O2 arena.
They went on to win best British group – making them the most successful band in the ceremony’s history.
Other awards went to James Bay, for best male, and Australian psych-rock band Tame Impala, who picked up best international group.
Canadian singer Justin Bieber, who performed his chart topping singles Love Yourself and Sorry, won best international male.
One Direction, who are officially on hiatus, also picked up best video for the space-themed Drag Me Down.
One Direction’s victory in the fan-voted best video category robbed Adele of the opportunity to become the most-garlanded artist in a single Brits ceremony.
The ceremony, at London’s O2 Arena, was broadcast live on ITV. You can also read live updates on the BBC News Website.